Real-valued Stability Analysis of Runge- Kutta-Chebyshev Methods for Delay Differential Equations

Standard

Real-valued Stability Analysis of Runge- Kutta-Chebyshev Methods for Delay Differential Equations. / Eremin, A. S.; Zubakhina, T. S.

International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2020. ed. / T.E. Simos; T.E. Simos; T.E. Simos; T.E. Simos; Ch. Tsitouras. American Institute of Physics, 2022. 090006 (AIP Conference Proceedings; Vol. 2425).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Eremin, AS & Zubakhina, TS 2022, Real-valued Stability Analysis of Runge- Kutta-Chebyshev Methods for Delay Differential Equations. in TE Simos, TE Simos, TE Simos, TE Simos & C Tsitouras (eds), International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2020., 090006, AIP Conference Proceedings, vol. 2425, American Institute of Physics, International Conference on Numerical Analysis and Applied Mathematics 2020, ICNAAM 2020, Rhodes, Greece, 17/09/20. https://doi.org/10.1063/5.0081530

APA

Eremin, A. S., & Zubakhina, T. S. (2022). Real-valued Stability Analysis of Runge- Kutta-Chebyshev Methods for Delay Differential Equations. In T. E. Simos, T. E. Simos, T. E. Simos, T. E. Simos, & C. Tsitouras (Eds.), International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2020 [090006] (AIP Conference Proceedings; Vol. 2425). American Institute of Physics. https://doi.org/10.1063/5.0081530

Vancouver

Eremin AS , Zubakhina TS. Real-valued Stability Analysis of Runge- Kutta-Chebyshev Methods for Delay Differential Equations. In Simos TE, Simos TE, Simos TE, Simos TE, Tsitouras C, editors, International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2020. American Institute of Physics. 2022. 090006. (AIP Conference Proceedings). https://doi.org/10.1063/5.0081530

Author

Eremin, A. S. ; Zubakhina, T. S. / Real-valued Stability Analysis of Runge- Kutta-Chebyshev Methods for Delay Differential Equations. International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2020. editor / T.E. Simos ; T.E. Simos ; T.E. Simos ; T.E. Simos ; Ch. Tsitouras. American Institute of Physics, 2022. (AIP Conference Proceedings).

BibTeX

@inproceedings{21300e4714a34c73b0946de7eaa67178,

title = "Real-valued Stability Analysis of Runge- Kutta-Chebyshev Methods for Delay Differential Equations",

abstract = "In the paper we consider first order stabilized Runge-Kutta-Chebyshev methods (RKCs) application to discrete delay differential equations (DDEs) and perform a linear stability analysis studying the standard linear test equation with real coefficients. We try two variants of RKCs extension for DDEs: the first, suitable for constant delays and constant time-steps; the second, with linear interpolation between the time-mesh points. It is shown that delay-independent stability regions are larger if using interpolation. As for ordinary differential equations RKCs have points of stability vanishing along the real values of the coefficient of the non-delayed term. We use damped RKCs to improve the stability regions and find an {"}optimal{"} damping factor to maximize the numerical stabiity region coverage of the exact stability domain. All the results are confirmed by numerical simulations.",

author = "Eremin, {A. S.} and Zubakhina, {T. S.}",

note = "Publisher Copyright: {\textcopyright} 2022 American Institute of Physics Inc.. All rights reserved.; International Conference on Numerical Analysis and Applied Mathematics 2020, ICNAAM 2020 ; Conference date: 17-09-2020 Through 23-09-2020",

year = "2022",

month = apr,

day = "6",

doi = "10.1063/5.0081530",

language = "English",

isbn = "9780735441828",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics",

editor = "T.E. Simos and T.E. Simos and T.E. Simos and T.E. Simos and Ch. Tsitouras",

booktitle = "International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2020",

address = "United States",

}

RIS

TY - GEN

T1 - Real-valued Stability Analysis of Runge- Kutta-Chebyshev Methods for Delay Differential Equations

AU - Eremin, A. S.

AU - Zubakhina, T. S.

PY - 2022/4/6

Y1 - 2022/4/6

N2 - In the paper we consider first order stabilized Runge-Kutta-Chebyshev methods (RKCs) application to discrete delay differential equations (DDEs) and perform a linear stability analysis studying the standard linear test equation with real coefficients. We try two variants of RKCs extension for DDEs: the first, suitable for constant delays and constant time-steps; the second, with linear interpolation between the time-mesh points. It is shown that delay-independent stability regions are larger if using interpolation. As for ordinary differential equations RKCs have points of stability vanishing along the real values of the coefficient of the non-delayed term. We use damped RKCs to improve the stability regions and find an "optimal" damping factor to maximize the numerical stabiity region coverage of the exact stability domain. All the results are confirmed by numerical simulations.

AB - In the paper we consider first order stabilized Runge-Kutta-Chebyshev methods (RKCs) application to discrete delay differential equations (DDEs) and perform a linear stability analysis studying the standard linear test equation with real coefficients. We try two variants of RKCs extension for DDEs: the first, suitable for constant delays and constant time-steps; the second, with linear interpolation between the time-mesh points. It is shown that delay-independent stability regions are larger if using interpolation. As for ordinary differential equations RKCs have points of stability vanishing along the real values of the coefficient of the non-delayed term. We use damped RKCs to improve the stability regions and find an "optimal" damping factor to maximize the numerical stabiity region coverage of the exact stability domain. All the results are confirmed by numerical simulations.

UR - http://www.scopus.com/inward/record.url?scp=85128568909&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/f57285fb-e1db-36f1-b799-83c74d58b25d/

U2 - 10.1063/5.0081530

DO - 10.1063/5.0081530

M3 - Conference contribution

AN - SCOPUS:85128568909

SN - 9780735441828

T3 - AIP Conference Proceedings

BT - International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2020

A2 - Simos, T.E.

A2 - Tsitouras, Ch.

PB - American Institute of Physics

T2 - International Conference on Numerical Analysis and Applied Mathematics 2020, ICNAAM 2020

Y2 - 17 September 2020 through 23 September 2020

ER -

ID: 95013993